The LHC (Large Hadron Collider) is a huge particle accelerator at CERN in Geneva, Switzerland. It consists basically of a circular tube with a circumference of 27 km, buried 100 m beneath the Swiss and French countryside, through which two beams of protons circulate in opposite directions. It accelerates these proton beams to the highest energy ever achieved on Earth for particles, and collides them together. When two protons collide, some of their kinetic (and mass) energy can be transformed into the mass of different particles. (This illustrates nicely how mass is just another form of energy, that can be transformed just like heat or potential energy.) We have built detectors to study the products of these collisions, which will allow us to study the forces of nature at their most fundamental level.a  An extremely useful unit for discussing the energy and mass of these particles is the electron-volt (eV). This is the amount of energy that an electron gains when falling through a potential difference of 1.0 V. In terms of units with which we are familiar: 1 eV = 1.60×10-19 J. Since E=mc2 for a particle at rest, we can refer to a particle’s mass in terms of its rest energy. What are these rest energies for the electron and the proton in Joules and eV if they have masses of 9.11×10-31 kg and 1.67×10-27 kg, respectively?b  At the LHC, protons will be accelerated to an energy of 7 TeV (7 x 1012 eV). What will be the momentum of these particles?c  Knowing the momentum, you can, in principle, calculate the speed of the protons. How would you go about doing this? Note: getting a numerical answer requires you to know a little calculus. I won’t expect you to do this – but give it a try if you’d like.d  Protons are actually made up of a collection of other particles (quarks and gluons), all bound together by the strong force. In a proton-proton collision, it is two of these constituents that are doing the actual colliding, and each of them carries only a fraction of the energy of the proton it is part of. The biggest success so for at the LHC is the discovery of the Higgs boson – a particle that is predicted by our theory, and which took many decades to find. Higgs particles can be made at the LHC by several processes, among them the annihilation of a quark from one proton and an anti-quark from the other. The energy that is released in this matter-antimatter explosion is then transformed into the mass of the newly created Higgs. Let’s assume that the Higgs has a rest energy of 200 GeV (2 x 1011 eV). How much energy, in total, do the quark and anti-quark need to make a Higgs boson at rest (assume that their masses are close to zero)? What fraction of the total available proton-proton energy is this?e  Would higher or lower quark-antiquark energies be required to make a Higgs that is not at rest? Why?